Correct Answer - Option 2 : III and IV
Given:
Average age of an ABC party leader and 9 followers = 29.7 years
Difference of ages of a leader and a follower = 47 years
The average age of the leader and a follower = A
Formula Used:
Average = Sum of values/Number of values
Calculation:
Let the age of leader be L years and the age of one follower be F years
Sum of ages of an ABC party leader and 9 followers = Average age of an ABC party leader and 9 followers × Number of persons
⇒ L + 9F = 29.7 × 10
⇒ L + 9F = 297 ---- (1)
L – F = 47 ---- (2)
Subtracting equation (2) from (1)
⇒ 10F = 250
⇒ F = 25 years
Put the value of F in equation (2)
L – 25 = 47
⇒ L = 72 years
Average age of leader and a follower = (L + F)/2
⇒ (72 + 25)/2
⇒ 97/2
⇒ 48.5
A = 48.5 years.
I. A is an integer
48.5 is not an integer
I is not correct
II. A – 19 = 32.3
48.5 – 19 = 29.5
II is not correct
III. A/5 = 9.7
48.5/5 = 9.7
III is correct
IV. Age of leader is 47 years more than the age of the follower.
L – F = 72 – 25
47
IV is correct.
∴ III and IV are correct.